Absolute convergence factors of Lipshitz class functions for general Fourier series
Classical Analysis and ODEs
2022-02-04 v1 Analysis of PDEs
Abstract
The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions Lip1 class provides absolute convergence of Fourier series. In particular we found special conditions for the functions of orthonormal system, for which the above sequences are absolute convergence factors of Fourier series of functions of Lip1 class. It is established that the resulting conditions are best possible in certain sense.
Keywords
Cite
@article{arxiv.2202.01555,
title = {Absolute convergence factors of Lipshitz class functions for general Fourier series},
author = {V. Tsagareishvili and G. Tutberidze},
journal= {arXiv preprint arXiv:2202.01555},
year = {2022}
}